Theoretical physicists have put forward many theoretical models to study the influence of magnetic fields
on strongly interacting systems, including lattice QCD [1]}, [2]}, [3]}, [4]}
and NJL model [5]}, [6]}, [7]}, [8]}, etc.,
while different models give completely different theoretical results.
For example, the lattice QCD simulation [1]} pointed out that quark and gluon deconfined
and chiral symmetry restoration occur together when a strong magnetic field is considered,
and the chiral phase transition temperature increases slightly with the increase of the magnetic fields,
so called magnetic catalytic(MC). However, Ref. [10]} studies the effect of magnetic fields
on quark propagators and points out that magnetic fields reduces quark condensation,
showing an inverse magnetic catalytic(IMC). According to the study of the NJL model [11]},
the quark condensation and dynamical chiral symmetry breaking are strengthened with increase of magnetic fields.
What are the properties and phase structure of QCD vacuum in the presence of a strong magnetic field?
Is it the magnetic catalytic? Or the inverse magnetic catalytic? It is an open question.
Therefore, it is very important to study the properties of QCD vacuum under magnetic fields
and its influence on the characteristic phase transition.
